• 충청수학회지
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• 제25권2호
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• pp.319-329
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• 2012

For a norm 1 function ${\sigma}$ in the Fourier-Stieltjes algebra of a locally compact group we define the space of ${\sigma}$-harmonic operators in the non-commutative $L^p$-space associated to the group von Neumann algebra of G. We will investigate some properties of the space and will obtain a precise description of it.

• 호남수학학술지
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• 제24권1호
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권1호
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• pp.71-78
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• 2013

Let X be a space and $2^X$(C(X);K(X);$C_K$(X)) denote the hyperspace of nonempty closed subsets(connected closed subsets, compact subsets, subcontinua) of X with the Vietoris topology. We investigate the relationships between the space X and its hyperspaces concerning the properties of connectedness im kleinen. We obtained the following : Let X be a locally compact Hausdorff space. Let $x{\in}X$. Then the following statements are equivalent: (1) X is connected im kleinen at $x$. (2) $2^X$ is arcwise connected im kleinen at {$x$}. (3) K(X) is arcwise connected im kleinen at {$x$}. (4) $C_K$(X) is arcwise connected im kleinen at {$x$}. (5) C(X) is arcwise connected im kleinen at {$x$}.

• 대한수학회지
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• 제36권4호
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• pp.737-746
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• 1999

We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

• 대한수학회보
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• 제32권1호
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• pp.85-91
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• 1995

For a locally compact Hausdorff space, we denote by $C_0(X)$ the Banach space of all continuous complex valued functions defined on X which vanish at infinity, equipped with the usual sup norm. In case X is compact, we write C(X) instead of $C_0(X)$. A well-known Banach-Stone theorem states that the existence of an isometry between the function spaces $C_0(X)$ and $C_0(Y)$ implies X and Y are homemorphic. D. Amir [1] and M. Cambern [2] independently generalized this theorem by proving that if $C_0(X)$ and $C_0(Y)$ are isomorphic under an isomorphism T satisfying $\left\$\mid$ T \right\$\mid$ \left\$\mid$ T^1 \right\$\mid$ < 2$, then X and Y must also be homeomorphic.

• 대한수학회지
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• 제35권4호
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• pp.803-829
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• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• 대한수학회보
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• 제35권3호
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 춘계학술대회 및 임시총회
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• pp.285-288
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• 2002

In this paper, we introduce the concept of a fuzzy almost c-continuity and investigate some of its properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제2권2호
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• pp.153-158
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• 2002

In this paper we introduce the concept of a fuzzy almost c-continuity and investigate some of its properties.

• 대한수학회지
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• 제46권4호
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• pp.813-826
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• 2009

In this paper, we generalize the notions of preserving and strongly preserving maps to arbitrary set based topological categories. Further, we obtain characterizations of each of these concepts as well as interprete analogues and generalizations of theorems of Gerlits at al [20] in the categories of filter and local filter convergence spaces.